The Al Nour Salafi party has boycotted the Abbasiya protest.
The Supreme Council said on its Facebook page Thursday that the clashes in Abbasiya were aimed at delaying the presidential elections and stalling the formation of a constituent assembly.
The Supreme Council also said that certain "unnamed" groups have used verses from the Quran calling for jihad, or holy war, to try to draw the military into an armed conflict.
The military had tried to persuade the protesters to move from their position near the Ministry of Defense to Tahrir Square, but they refused, the Facebook statement said.
Controversy about the approaching presidential elections has been growing.
The Muslim Brotherhood's preferred candidate, Khairat El Shater, who was disqualified from running last month, was referred to the country's general prosecutor Friday for insulting the election commission.
Abu Ismael was also referred to the general prosecutor for alleged forgery. He was disqualified from standing because of evidence that his late mother had U.S. citizenship, an assertion he has denied.
On Thursday, three other presidential candidates also were referred for alleged violations of election campaign law.
The three candidates -- leading independent Abdel Monein Aboul Fettouh; Mohamed Mursi of the Islamist Freedom and Justice Party; and Amre Moussa -- were accused of breaking the law by holding meetings on college campuses.
"These infringements by the presidential candidates will be taken very seriously, and they will be questioned as soon as possible. They could be fined," Adel Saeed, the official spokesman for the general prosecutor, told CNN on Thursday.
The election commission has disqualified about 10 of the 23 presidential contenders, its chief has said. The disqualifications have prompted widespread anger.
International powers urged all sides to exercise restraint after the clashes Wednesday.
Assailants targeted the protesters in Cairo early Wednesday, medical sources said. At least 150 people were injured, Dr. Ahmed Thabet, a physician working in a field hospital near where the clashes took place, said Thursday.
It was unclear who the attackers were, but they were not wearing uniforms, witnesses said.
The Freedom and Justice Party blamed the Supreme Council for the deaths and injuries in the Abbasiya clashes, and it said that the council, not the protesters, wants to delay the transition of power.
A government official denied reports that the military was involved in Wednesday's violence.
Clashes have erupted in Egypt since an uprising led to the toppling of Mubarak in February of last year, with protesters demanding the military leaders who took over hand over power to a civilian administration.